Question

When a bird of weight $W$ sis on a stretched wire, the tension $T$ in the wire is:

• A. $>W/2$
• B. $=W$
• C. less than $W$
• D. $Noneofthese$

Answer 1

The correct option is A $>W/2$

Given that,

Weight of bird = W

According to figure

If there is no horizontal or vertical motion of the bird and string, the forces along in the horizontal direction and in the vertical direction must individually sum to zero.

So now,

$T\cos \theta =T\cos \theta .....\left(I\right)$

$2T\sin \theta =W....\left(II\right)$

Now, from equation (II)

$2T\sin \theta =W$

$T=\frac{\frac{W}{2}}{\sin \theta }$

$T=\frac{W}{2}$

For, values of sin θ lying between 0 and 1, the tension in the rope will always be greater than $\frac{W}{2}$

Hence, the tension is greater than $\frac{W}{2}$